dd63489a-78ad-4cc5-86f8-09b40e0e6e45 16 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

randi function as in Octave_rang_m_n randi i 1_m range j 1_n range a i j el_rang 1 el_rang 2 el 100 *_rang 1 el 100 * - random 100 / 0 round + : for for a 21 line :

Echelon form of a given matrix_M echelon ech_M : temp_p 1 : gen 1_M rows_M cols 12 mat min range isZero 0 ech cols matrix : isNotZero 0 ech cols matrix : mod_rows 0 ech cols matrix : i 1 ech rows range ech i row gen el 0 ≡ (i temp_p ≥ (& isZero isZero ech i row stack : 11 line isNotZero isNotZero ech i row stack : 11 line if 11 line for ech isNotZero isZero stack : pivot temp_p : pivot_row ech pivot row : pivot_row gen el 0 ≠ pivot_row pivot_row pivot_row gen el / : temp_p pivot 1 + : 21 line continue 11 line if j pivot 1 + (ech rows range gen ech rows ≡ (pivot 1 > (& continue 11 line to_stack ech j row ech j row gen el pivot_row * - : mod_rows mod_rows to_stack stack eval : 21 line if 11 line for M1 pivot 1 > ech 1 pivot 1 - 1 ech cols submatrix 0 ech cols matrix if : M2 pivot_row : M3 mod_rows : ech M1 M2 M3 stack : 131 line for ech 41 line :

Row Reduced Echelon Form (RREF)_M rref_eM_M echelon : pivot 0_M cols matrix : i 1_eM rows range_eM i row 1_eM cols matrix ≠ pivot pivot_eM i row stack eval : 11 line continue 11 line if 11 line for temp pivot reverse eval : i 1 temp rows range j 1 temp cols range temp i j el 0 ≠ pos i el j : break 21 line continue 11 line if 11 line for 11 line for result_p temp 1 row : i 2 temp rows range row_mod temp i row : k 1 i 1 - (range sust_p temp i row pos k el (el result_p k row * : row_mod row_mod sust_p - : 21 line for result_p result_p row_mod stack eval : 31 line for result_f result_p reverse eval_eM rows temp rows -_eM cols matrix stack : 81 line :

Random matrix A 5 - 521 mat 1010 randi :

tic 0 time :

A 21 - 321401 - 261 - 534 mat :

A rref 100 5.667 010 1.667 - 001 3.667 - 34 mat ≡

A 21 - 3140261 - 33 mat :

Row reduced echelon form A rref #

toc 0 time :

toc tic - 0.12 s *